MinT - Best Known (9, 9+7, s)-Nets in Base 3

Best Known (9, 9+7, s)-Nets in Base 3

(9, 9+7, 34)-Net over F₃ — Constructive and digital

Digital (9, 16, 34)-net over F₃, using

3² times duplication [i] based on digital (7, 14, 34)-net over F₃, using
- linear code embedding found in a computer search [i]

(9, 9+7, 41)-Net over F₃ — Digital

Digital (9, 16, 41)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁶, 41, F₃, 2, 7) (dual of [(41, 2), 66, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁶, 82, F₃, 7) (dual of [82, 66, 8]-code), using
  - generator matrices provided on Edelâ€™s homepage [i]

(9, 9+7, 218)-Net in Base 3 — Upper bound on s

There is no (9, 16, 219)-net in base 3, because

1 times m-reduction [i] would yield (9, 15, 219)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 14 487435 > 3¹⁵ [i]